The Russian leader, a former KGB intelligence officer, is not given to unguarded moments or admissions of guilt.
Flynn was paid $45,000 to speak at the event and was in the "seat of honor" next to the Russian president. "There is a theory that Kennedy's assassination was arranged by US intelligence services", the Russian president added. "That's why, in the grand scheme of things, we don't care who's the head of the United States", Putin said.
The FBI also is probing whether anyone associated with Trump's presidential campaign was involved in the Russian hacking.
Putin also maintained that he was unaware of any contact between Jared Kushner and the Kremlin, despite the latter being under investigation for reportedly setting up a back-channel for secret communication. "I don't know the routine job of an ambassador".
"I want to say that Russian Federation is developing along a democratic path. There was not even a specific discussion of sanctions or something else", Putin said.
"I just find it fantastic how you created a sensation where there wasn't anything at all. And out of this sensation you created a weapon of war against the president", he said, referring to Trump.
There is a widely-seen photograph of Flynn and Putin sitting at the same banquet table in Moscow in 2015 when the retired Army general was a Trump advisor. But Putin didn't give anything by way of evidence with the speculation. There's nothing to even talk about.
Mr Putin said the U.S. intelligence agencies had been misled over their findings. "Do you even understand what you're asking or not?"
Did Russian President Vladimir Putin collect damaging information on President Donald Trump? Putin, slouched over in his seat, scoffed at the idea. Do you think, an ambassador from any place in the world or from the U.S. reports to me daily as to whom he meets with and what they discuss? Are you all have you all lost your senses over there?.
But Michael McFaul, U.S. ambassador in Moscow from 2012 to 2014 and now an NBC News analyst, said in April: "It is not coincidence that Flynn was placed next to President Putin". There can even be hackers, by the way, in the United States.
"That's all there is to it", Putin added.
"Why do you feel you have the right to ask us these kinds of questions?" He then suggested that hackers from within the United States could also have been responsible, and used Russian Federation as a fall guy.
"Point your finger to any spot on the world's map, everywhere you'll hear complaints that American officials interfere in their political domestic processes".
USA intelligence agencies concluded in January that Moscow tried to tilt the election campaign in Mr Trump's favour, including by hacking into the e-mails of senior Democrats, a charge the Kremlin denies. When Kelly told him that sounded like a "justification", he argued that it was a "statement of fact".